Key takeaways
A percentage of a percentage is just multiplication in disguise. Convert both to decimals, multiply, and convert back.
- Convert to decimals, multiply, convert back.
- 20 % of 50 % is 10 %, not 70 % and not 30 %.
- This is how compound rates and conditional survey results work.
The one-line answer
20 % of 50 % is 0.20 × 0.50 = 0.10, which is 10 %.
Where it appears
- Surveys: 60 % of respondents own a car, and 25 % of those drive daily. Daily drivers are 0.60 × 0.25 = 15 % of everyone.
- Tax on tax: a 10 % surcharge on a 20 % tax adds 2 points, not 10.
- Interest: a 5 % rate "reduced by 10 %" becomes 4.5 %.
The common mistake
People add or subtract when they should multiply. "Half of 30 %" is 15 %, and "30 % less than 30 %" is 21 %, because 30 % × 0.70 = 21 %.
Related questions
- What is 40 % of 25 %?
